The linear speed (v) is simply the rate at which the body is moving along that circular path given by the product of the radius (r) and the angular speed or:
v
=
r
Answer and Explanation:
The spinning record has the following characteristics:
Diameters
=
d
=
6.3
in
Frequency
=
f
=
45
rev
min
To find the angular velocity
(
)
in radians per minute, multiply the frequency with
2
π
rad
:
=
2
π
f
=
(
2
π
rad
)
(
45
rev
min
)
=
90
π
rad
min
=
282.7433
≈
283
rad
min
The linear velocity of the point on the edge of the record uses the radius or half of the diameter which is:
r
=
d
2
=
6.3
in
2
=
3.15
in
The linear velocity (v) comes from the multiplication of the radius and frequency which gives:
Answers & Comments
)
the product of
1
π
and the frequency (f) or:
=
2
π
f
The linear speed (v) is simply the rate at which the body is moving along that circular path given by the product of the radius (r) and the angular speed or:
v
=
r
Answer and Explanation:
The spinning record has the following characteristics:
Diameters
=
d
=
6.3
in
Frequency
=
f
=
45
rev
min
To find the angular velocity
(
)
in radians per minute, multiply the frequency with
2
π
rad
:
=
2
π
f
=
(
2
π
rad
)
(
45
rev
min
)
=
90
π
rad
min
=
282.7433
≈
283
rad
min
The linear velocity of the point on the edge of the record uses the radius or half of the diameter which is:
r
=
d
2
=
6.3
in
2
=
3.15
in
The linear velocity (v) comes from the multiplication of the radius and frequency which gives:
v
=
r
v
=
(
3.15
in
)
(
90
π
rad
min
)
v
=
890.641
≈
891
in
min
This means that the angular speed is
=
283
rad
min
and the linear velocity is
v
=
891
in
min
.
Verified answer
Solution:
The angular velocity is already given, that is 45 revolutions per second. We are required to convert the unit to radians per second. Therefore,
[tex]\sf 45\;\dfrac{rev}{s} \times\dfrac{2\pi\;rad}{1\;rev} =282.7\;radians\;per\;second45 [/tex]
Note: 1 revolution is equal to 2π radians (about 6.283 radians).
[tex] \: [/tex]
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